ABSTRACT A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent: 1. B is regular; 2. the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B; 3. B is isomorphic to a bilattice of the form L 1 · L 2 (...) where L 1 and L 2 are bounded lattices. We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation. (shrink)

Bilattices, introduced by Ginsberg as a uniform framework for inference in artificial intelligence, are algebraic structures that proved useful in many fields. In recent years, Arieli and Avron developed a logical system based on a class of bilattice-based matrices, called logical bilattices, and provided a Gentzen-style calculus for it. This logic is essentially an expansion of the well-known Belnap–Dunn four-valued logic to the standard language of bilattices. Our aim is to study Arieli and Avron’s logic from the perspective of (...) abstract algebraic logic . We introduce a Hilbert-style axiomatization in order to investigate the properties of the algebraic models of this logic, proving that every formula can be reduced to an equivalent normal form and that our axiomatization is complete w.r.t. Arieli and Avron’s semantics. In this way, we are able to classify this logic according to the criteria of AAL. We show, for instance, that it is non-protoalgebraic and non-self-extensional. We also characterize its Tarski congruence and the class of algebraic reducts of its reduced generalized models, which in the general theory of AAL is usually taken to be the algebraic counterpart of a sentential logic. This class turns out to be the variety generated by the smallest non-trivial bilattice, which is strictly contained in the class of algebraic reducts of logical bilattices. On the other hand, we prove that the class of algebraic reducts of reduced models of our logic is strictly included in the class of algebraic reducts of its reduced generalized models. Another interesting result obtained is that, as happens with some implicationless fragments of well-known logics, we can associate with our logic a Gentzen calculus which is algebraizable in the sense of Rebagliato and Verdú . We also prove some purely algebraic results concerning bilattices, for instance that the variety of distributive bilattices is generated by the smallest non-trivial bilattice. This result is based on an improvement of a theorem by Avron stating that every bounded interlaced bilattice is isomorphic to a certain product of two bounded lattices. We generalize it to the case of unbounded interlaced bilattices. (shrink)

Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further (...) extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective. (shrink)

The assumption that it is possible to distinguish pure syntax from any semantic interpretation is common to contemporary extensionalist approaches to philosophy of language, mind, cognitive science, and artificial intelligence. The origin of the term 'pure syntax' is traced to Carnap's distinction between pure and applied syntax and semantics, and to formalist analyses of mathematical systems as uninterpreted token manipulating games. It is argued in opposition to this trend that syntax can never be purified entirely of semantics, (...) that there can be no such thing as meaningless syntactical tokens or uninterpreted symbols, but that tokens must always betoken and symbols always symbolize something. The implications of the myth of pure syntax in rule-structured and connectionist artificial intelligence, semantic network processing, and their philosophical-psychological rationales, are explored. The fact that rule-structured artificial intelligence in principle can simulate any connectionist model, and that rule-structured artificial intelligence presupposes the myth of pure syntax links the myth to traditional approaches and new paradigms in cognitive engineering. (shrink)

Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap’s four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result (...) provides a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke/Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap’s logic, the logic given by the simplest bilattice. (shrink)

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, (...) or in social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

This paper presents an information-based logic that is applied to the analysis of entailment, implicature and presupposition in natural language. The logic is very fine-grained and is able to make distinctions that are outside the scope of classical logic. It is independently motivated by certain properties of natural human reasoning, namely partiality, paraconsistency, relevance, and defeasibility: once these are accounted for, the data on implicature and presupposition comes quite naturally.The logic is based on the family of semantic spaces known as (...) bilattices, originally proposed by Ginsberg (1988), and used extensively by Fitting (1989, 1992). Specifically, the logic is based on a subset of bilattices that I call evidential bilattices, constructed as the Cartesian product of certain algebras with themselves. The specific details of the epistemic agent approach of the logical system is derived from the work of Belnap (1975, 1977), augmented by the use of evidential links for inferencing. An important property of the system is that it has been implemented using an extension of Fitting's work on bilattice logic programming (1989, 1991) to build a model-based inference engine for the augmented Belnap logic. This theorem prover is very efficient for a reasonably wide range of inferences. (shrink)

While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. Thus, with (...) little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections. (shrink)

Scholarly debates on the Critique of Pure Reason have largely been shaped by epistemological questions. Challenging this prevailing trend, Kant's Reform of Metaphysics is the first book-length study to interpret Kant's Critique in view of his efforts to turn Christian Wolff's highly influential metaphysics into a science. Karin de Boer situates Kant's pivotal work in the context of eighteenth-century German philosophy, traces the development of Kant's conception of critique, and offers fresh and in-depth analyses of key parts of the (...) Critique of Pure Reason, including the Transcendental Deduction, the Schematism Chapter, the Appendix to the Transcendental Analytic, and the Architectonic. The book not only brings out the coherence of Kant's project, but also reconstructs the outline of the 'system of pure reason' for which the Critique was to pave the way, but that never saw the light. (shrink)

Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiple-valued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to logic programming languages that can, at least in principle, be implemented. Appropriate bilattice background information is presented, so the paper is relatively self-contained.

This is an exploratory paper whose aim is to investigate the potentialities of bilattice theory for an adequate definition of the deduction apparatus for multi-valued logic. We argue that bilattice theory enables us to obtain a nice extension of the graded approach to fuzzy logic. To give an example, a completeness theorem for a logic based on Boolean algebras is proved.

In a previous work we studied, from the perspective ofAlgebraic Logic, the implicationless fragment of a logic introduced by O. Arieli and A. Avron using a class of bilattice-based logical matrices called logical bilattices. Here we complete this study by considering the Arieli-Avron logic in the full language, obtained by adding two implication connectives to the standard bilattice language. We prove that this logic is algebraizable and investigate its algebraic models, which turn out to be distributive bilattices with (...) additional implication operations. We axiomatize and state several results on these new classes of algebras, in particular representation theorems analogue to the well-known one for interlaced bilattices. (shrink)

According to one historic view of liberal education, such education is incompatible with the express pursuit of civic goods. Call that view ‘pure liberal education’. Students engaged in pure liberal education are set free, temporarily, from utilitarian concerns, for a course of study aimed at intrinsic goods—most notably knowledge but also the formation of a virtuous mind. Proponents claim that a direct pursuit of civic goods would compromise the mode, matter, and/or integrity of pure liberal education—that is, (...) its freedom from utilitarian concern, its wide-ranging and intrinsically valuable subject matter, and its commitment to following the truth wherever it leads. In reply, I offer a pedagogy that requires (almost) no departure from the pure liberal ideal yet which reserves a modest, though important, place for civic formation. That place emerges from the fact that academic and civic life ‘overlap’ in an important respect: both involve a conversation and thus a common set of virtues. The latter consist in those practices and dispositions that enable the conversation to go well, by encouraging mutual understanding and the formation of true beliefs. The existence of this overlap provides a way for pure liberal educators, who already expressly influence their students’ academic formation, to likewise influence their civic formation. It consists in teachers consciously developing those virtues in their students, along with an awareness of the virtues’ relevance for civic life. This pedagogy retains the matter and integrity of pure liberal education, with only brief introductions of the practical mode. (shrink)

Taylor has recently argued that adopting either the standard Kimian or Davidsonian approaches to the metaphysics of events quite directly solves the regress of pure powers. I argue, though, that on closer inspection Taylor’s proposal does not succeed, given either the Kimian or the Davidsonian account of events.

I explore a strand of reception history that follows Rudolf Carnap’s shift from a purely syntactical analysis of constructed languages to his conception of pure semantics. My exploration focuses on Gustav Bergmann’s and Everett Hall’s interpretation of pure semantics, their understanding of what constitutes a ’formal’ investigation of language, and their arguments concerning the relationship between expressions and their extra-linguistic referents. I argue that Bergmann and Hall strongly misread Carnap’s semantic project and, subsequently, their misunderstanding is passed down (...) through colleagues and students. (shrink)

This chapter considers Kant's relation to Hume as Kant himself understood it when he wrote the Critique of Pure Reason and the Prolegomena. It first seeks to refine the question of Kant's relation to Hume's skepticism, and it then considers the evidence for Kant's attitude toward Hume in three works: the A Critique, Prolegomena, and B Critique. It argues that in the A Critique Kant viewed skepticism positively, as a necessary reaction to dogmatism and a spur toward critique. In (...) his initial statement of the critical philosophy Kant treated Hume as an ally in curbing dogmatism, but one who stopped short of what was really needed: a full critique of reason, to establish the boundaries of metaphysical cognition. Kant found fault with Hume's analyses of cognition and experience, and specifically his failure to see the crucial importance of synthetic a priori cognition in metaphysics. In particular, he held that Hume's empiricist account of cognition could neither explain the synthetic a priori cognition actually found in mathematics and natural science, nor provide a principled account of the limits on what can be known--and what can be thought--through the pure concepts of the understanding. According to Kant, Hume therefore failed in his attempt to determine the limits of metaphysics, whereas he was able to succeed because his transcendental philosophy provided a thorough account of cognition, its structure and limits. In the Prolegomena and the B Critique Kant distinguished his position more sharply from Hume's. He also adopted a more negative attitude toward "skeptical idealism" than before; but he attributed such skepticism to Descartes, not Hume. Prior to the B Critique Kant did not see Hume as attacking natural science or ordinary cognition. In none of the three works was Kant's main aim to "answer the skeptic." His primary aim was to firmly establish the boundary of metaphysics, by discovering the elements of human cognition and fixing its proper domain. His purported discoveries about the limits of metaphysical cognition meant that the traditional objects of metaphysical knowledge, God, the soul, and the world as it is in itself, are unknowable, hence that traditional metaphysics itself is impossible. Besides settling the possibility or impossibility of metaphysics, his findings would also prevent the illegitimate extension of principles of sensibility to God and the noumenal self, an extension that would threaten the metaphysics of morals by incorrectly denying the thinkability of noumenal freedom, and that might otherwise lead to "materialism, fatalism, atheism, and freethinking unbelief" (B xxxiv). (shrink)

This paper presents Fichte’s system of philosophical science with the aim of elucidating the boundary separating the pure, absolute I and the empirical, individual I in the system. Tapping on writings related to the two versions of the Jena Doctrine of Science, I represent Fichte’s philosophical project as the primarily epistemological one of maintaining the scientific status of pre-philosophical knowledge in the face of the Maimonian skeptical challenge. Apparently, Fichte analyzes the scientificity of a body of knowledge in terms (...) of its certainty and systematicity. But it is in connection with his conception of a philosophical-scientific system as a presentation of an autonomous “system of a human mind” that we are able to make sense of the systematicity and certainty that are at play in the concept. Moreover, the philosophical-scientific system falls short of meeting the Maimonian skeptical challenge so long as it remains incomplete. Most importantly, the human-mental system is no empirical subject, but a pure subject that maps the possible perceptions and actions which an empirical subject has the potential to realize for itself. (shrink)

In contrast to Hintikka’s enormously complex distributive normal forms of first- order logic, this paper shows how to generate minimized disjunctive normal forms of first-order logic. An effective algorithm for this purpose is outlined, and the benefits of using minimized disjunctive normal forms to explain the truth conditions of propo- sitions expressible within pure first-order logic are presented.

The ArgumentIn the minds of many, the Bourbakist trend in mathematics was characterized by pursuit of rigor to the detriment of concern for applications or didactic concessions to the nonmathematician, which would seem to render the concept of a Bourbakist incursion into a field of applied mathematices an oxymoron. We argue that such a conjuncture did in fact happen in postwar mathematical economics, and describe the career of Gérard Debreu to illustrate how it happened. Using the work of Leo Corry (...) on the fate of the Bourbakist program in mathematics, we demonstrate that many of the same problems of the search for a formalstructurewith which to ground mathematical practice also happened in the case of Debreu. We view this case study as an alternative exemplar to conventional discussions concerning the “unreasonable effectiveness” of mathematics in science. (shrink)

This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and (...) track-down operations allow settling positively the question of whether bilattice-based semantics are available for subsystems of S_fde. (shrink)

One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artificial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while (...) making the mathematical machinery simpler and more perspicuous. In addition, work such as that of Yablo fits naturally into the bilattice setting. What I do here is present the general background of bilattices, discuss why they are natural, and show how fixpoint approaches to truth in languages that allow self-reference can be applied. This is not new work, but rather is a summary of research I have done over many years. (shrink)

The present article focuses on the antinomy of pure practical reason and the deduction of the Highest Good in the Dialectic of Pure Practical Reason (in the second Critique). Although Kant claims that the Dialectic contains both the antinomy and the deduction, the boundaries dividing one from the other are at best vague. It is difficult to make out where the antinomy of practical reason ends and where the deduction begins. To locate both and to distinguish one from (...) the other (with special attention paid to the modality of the Highest Good) are the chief aims of this article. Additionally but no less importantly, I show, against the line of criticism originally traceable to Schopenhauer, that the antinomy of practical reason amounts to more than a reflection of Kant’s “architectonic obsession.” Not only does the antinomy of practical reason correspond to a genuine dialectical problem in the Critique of Practical Reason, but it also shares a fundamental (even if not immediately apparent) similarity with the antinomy of pure speculative reason. Finally, I consider Kant’s transcendental deduction of the Highest Good against the backdrop of his other deductions, especially the deduction of the categories in the Critique of Pure Reason, and defend it against the charge of potential circularity. (shrink)

The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our (...) work. The outcome are paraconsistent logics with a lot of desirable properties.1. (shrink)

We introduce a new product bilattice con- struction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lat- tice factors. Finally, we (...) show how to employ our product construction to define first-order definable classes of bi- lattices corresponding to any first-order definable subclass of residuated lattices. (shrink)

This paper discusses the idea of "pure experience" within the context of the Buddhist tradition and in connection with the notions of emptiness and dependent origination via a reading of Dale Wright's reading of 'Huangbo' in his 'Philosophical Meditations on Zen Buddhism'. The purpose is to appropriate Wright's text in order to engender a response to Steven Katz's contextualist-constructivist thesis that there are no "pure" (i.e., unmediated) experiences. In light of the Mahayana claim that everything is empty of (...) substance, i.e., originates dependently through conditions, contingencies, and contexts, what does the "purity" of the Enlightenment experience mean for Chan/Zen Buddhism? (shrink)

In this paper we reexamine the question of whether questions areinherently intensional entities. We do so by proposing a novelextensional theory of questions, based on a re-interpretation of thedomain of t as a bilattice rather than the usual booleaninterpretation. We discuss the adequacy of our theory with respect tothe adequacy criteria imposed on the semantics of questionsby (Groenendijk and Stokhof 1997). We show that the theory is able to account in astraightforward manner for some complex issues in the semantics (...) ofquestions including coordinated questions, combined indicative andinterrogative sentences, questions with quantifiers, and theimpossibility of negating questions. (shrink)

This dissertation defends and develops the thesis that some instances, or tokens, of dispositional properties are pure. A pure disposition has no causal basis in any further properties beyond the disposition. A causal basis typically consists of some set of properties underlying a disposition that enables the disposition to manifest when stimulated in the appropriate circumstances. For example, a vase is fragile because it is disposed to break when a hammer or other suitable object strikes it, where the (...) causal basis for fragility is the underlying micro-structure of the vase. Moreover, micro-structural properties of the vase seem to anchor the continuous existence of the vase’s fragility when the vase is not actually breaking. In contrast to the neo-Humean metaphysical assumption that any disposition requires a causal basis in further properties, as in the example of fragility, the Pure Dispositions Thesis denies this. This dissertation achieves four goals. First, it defends the Pure Dispositions Thesis from notable objections: the Powers Regress Argument, the Insufficient Causal Basis Argument, the Argument from the Identity Thesis, and the Argument from Spatial Occupation. Second, it evaluates several theories of the continuous existence of pure dispositions, and argues that some pure dispositions are self-grounded via a minimally sufficient occurrence of their own power. Third, it presents two arguments that some pure dispositions are extrinsically grounded, the Argument from the Higgs Field and the Argument from Priority Monism, and deflects numerous objections to those arguments. Finally, it develops and defends an account of systems of pure dispositions, arguing that a pure dispositional system may generate higher-level categorical and dispositional properties by way of an emergence mechanism involving the union of two pure dispositions. (shrink)

The article treats as significant the formal coincidence between Kant’s presentation of the science of metaphysics in the “Architectonic of Pure Reason” chapter of the first Critique and Alexander Baumgarten’s presentation of the same in the Metaphysica. From his comments on Baumgarten in the metaphysics lectures, the article shows that for Kant metaphysics in its traditional form lacked completeness and systematic order. Kant fits completeness into his architectonic plan of a scientific metaphysics by converting Baumgartian ontology into an “analytic (...) of the understanding”; Kant achieves the systematicity by modeling a rational “idea of the form of the whole” after Baumgarten’s tree-like ordering of the special sciences of metaphysics. Thus, Kant realizes the completeness and systematicity in a theoretical presentation of the science of metaphysics that he finds lacking in Baumgarten precisely by borrowing from the latter his scheme for metaphysics. (shrink)

As early as 1981, about 1 year before Shechtman’s discovery of an actual quasicrystal, Alan L. Mackay discussed, in a seminal paper, the first steps for the expansion of crystallography toward its modern phase. In this phase, new possibilities of structures and order, such as the structures of five-fold symmetry, for crystals have been discovered. Medieval Islamic decorators as well as Albrecht Dürer, Johannes Kepler, Roger Penrose, Mackay himself, and other pioneer crystallographers raised important contributions to the theoretical discovery of (...) crystalline possibilities long before or independently of the discovery of their actual existence. In this paper, I discuss further the philosophical significance of Mackay’s theoretical discovery and his contribution to the expansion of pure geometrical crystallography, biological crystallography, and generalized crystallography. (shrink)

My response to Gabriele Gava’s Kant’s Critique of Pure Reason and the Method of Metaphysics (2023) focuses on Kant’s conception of the role of critique in the Critique of Pure Reason. On my account, Gava’s emphasis on the constructive elements of the Critique downplays the critique of former metaphysics elaborated in all three parts of the Transcendental Doctrine of Elements. After some comments on Kant’s conception of the Critique as a doctrine of method, I support this view by (...) discussing the relation between transcendental philosophy and transcendental critique, Kant’s analysis of the faculties, and his transcendental deduction of space. (shrink)

According to Humeanism, actions cannot be adequately explained without reference to the desires of an agent. Desires are viewed as sources of motivation or as motivating states and thus as having an indispensable role to play in the explanation of actions. One of the main rivals of Humeanism is pure cognitivsm. According to this view, actions are to be explained exclusively by beliefs. The present paper's focus is on arguments Jonathan Dancy has put forward in favor of this (...) class='Hi'>pure cognitivist picture. His main line of argument tries to convince us of the claim that desires have no explanatory value at all as regards the explantion of an agent's actions. I argue that none of Dancy's arguments against Humeanism is successful, and moreover that the pure cognitivists position fails on its own terms because pure cognitivism is unable to provide an account of desires that makes intelligible their role in the mental economy of agents. (shrink)

The aims of the paper are (i) to introduce a framework for reasoning about equity in health distribution before and after interventions, and (ii) to assess various Gini measures applied to healthy life expectancy against explicit normative concerns. Part 1 discusses different ways of measuring pure health inequality and suggests that a modified Gini measure could be used to measure inequity in health before and after treatment. Part 2 introduces a framework for reasoning about distributions of health. Part 3 (...) discusses three normative concerns that any acceptable measure of inequity should satisfy. Part 4 describes the standard Gini measure for measuring pure inequalities in healthy life expectancy. It also examines Wagstaff's Extended Gini measure of health inequity and discusses how it can be used to make priority weights to the worst off explicit. The final section expresses some programmatic worries and possible applications. It is argued that the impact of interventions should be evaluated both in terms of reduced inequity (as measured by the Extended Gini or the Extended Proportional Gini) and improved efficiency (measured by gains in average healthy life expectancy). Measurement of pure health inequity could supplement cost-effectiveness analysis as a basis for fair priority setting. (shrink)

Two philosophers, Robert Spaemann and Henri Gouhier, have identified a similarity between Fénelon and Kant in the prominence of motive in their thought: disinterestedness in Fénelon's pure love and in Kant's good will. Spaemann emphasizes their common detaching of the ethical in terms of motivation from the context of happiness. In this article I explore further similarities and differences under the topics of perfectionism, pure love, good will, happiness, and disinterestedness, as these are pertinent to their thought. On (...) perfectionism there appears a stark contrast; on pure love over against good will, on happiness, and on disinterestedness, however, there seems a balance between likenesses and differences. Finally I point out a qualification set on pure love by Fénelon and on the good will by Kant. (shrink)

Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem (...) with respect to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics. (shrink)

Kant is the central figure of modern philosophy. He sought to rebuild philosophy from the ground up, and he succeeded in permanently changing its problems and methods. This revised edition of the Prolegomena, which is the best introduction to the theoretical side of his philosophy, presents his thought clearly by paying careful attention to his original language. Also included are selections from the Critique of Pure Reason, which fill out and explicate some of Kant's central arguments, and in which (...) Kant himself explains his special terminology. The first reviews of the Critique, to which Kant responded in the Prolegomena, are included in this revised edition. The volume is completed by a historical and philosophical introduction, explanatory notes, a chronology, and a guide to further reading. (shrink)

This classic text, written by philosopher and mathematician William Thomson, presents a systematic exposition of the laws of thought and their role in science, logic, and philosophy. The book is still widely used in philosophy and mathematics courses today. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within (...) the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)